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应用数学和力学（英文版）
应用数学和力学（英文版）

周哲玮

月刊

0253-4827

amm@department.shu.edu.cn

021-66135601，66135219

200444

上海市上大路99号

应用数学和力学（英文版）/Journal Applied Mathematics and MechanicsCSCDEISCI
查看更多>>1980年5月由我国著名科学家、上海大学校长钱伟长院士创办。创刊至2002年底，钱伟长院士一直亲自担任主编。2003年改由我校副校长、博导周哲玮教授担任主编。钱伟长院士亲自制定办刊的宗旨是：发表力学、力学中的数学方法和近代力学密切相关的应用数学的创造性学术性论文。所谓创造性学术论文是指具有新思想、新观点、新方法的原创性学术论文。我刊对应的中文版由重庆交通大学主办并出版。英文版由上海大学主办，上海大学出版社出版。国外由德国Springer出版社发行。我刊的读者对象主要是从事与力学和应用数学有关的科研人员、工程技术人员和大专院校师生。被收录的数据库《科学引文索引（扩大版）》（SCIE）、《工程索引》（EI Compendex）、《世界译文索引》、美国《数学评论（MR）》、《应用力学评论（AMR）》、《力学》、《宇航文摘》、《当代数学》、俄罗斯《文摘杂志》力学、数学专辑，德国《数学文摘》及中国《中国力学文摘》、《中国数学文摘》、《中国物理文摘》、中国科技期刊光盘版《中国期刊网》、中国台湾《中文电子期刊服务数据库（CEPS）》、中国西南信息研究中心《中文科技期刊数据库》、中国信息研究所《万方数据库——数字化期刊群》等21种国内外权威文摘刊物及其数据库均收录我刊全文、题录和文摘。《应用数学和力学》被美国力学科学院评为17种国际力学刊物之一。
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    A novel efficient energy absorber with free inversion of a metal foam-filled circular tube

    Jianxun ZHANGJinwen BAI
    1-14页
    查看更多>>摘要：In this paper,a novel efficient energy absorber with free inversion of a metal foam-filled circular tube(MFFCT)is designed,and the axial compressive behavior of the MFFCT under free inversion is studied analytically and numerically.The theoretical analysis reveals that the energy is mainly dissipated through the radial bending of the metal circular tube,the circumferential expansion of the metal circular tube,and the metal filled-foam compression.The principle of energy conservation is used to derive the theoretical formula for the minimum compressive force of the MFFCT over free inversion under axial loading.Furthermore,the free inversion deformation characteristics of the MFFCT are analyzed numerically.The theoretical steady values are found to be in good agreement with the results of the finite element(FE)analysis.The effects of the average diameter of the metal tube,the wall thickness of the metal tube,and the filled-foam strength on the free inversion deformation of the MFFCT are considered.It is observed that in the steady deformation stage,the load-carrying and energy-absorbing capacities of the MFFCT increase with the increase in the average diameter of the metal tube,the wall thickness of the metal tube,or the filled-foam strength.The specific energy absorption(SEA)of free inversion of the MFFCT is significantly higher than that of the metal tube alone.
      原文链接:
    • 万方数据
    • 维普

    Dirac method for nonlinear and non-homogenous boundary value problems of plates

    Xiaoye MAOJiabin WUJunning ZHANGHu DING...
    15-38页
    查看更多>>摘要：The boundary value problem plays a crucial role in the analytical investi-gation of continuum dynamics.In this paper,an analytical method based on the Dirac operator to solve the nonlinear and non-homogeneous boundary value problem of rectan-gular plates is proposed.The key concept behind this method is to transform the nonlin-ear or non-homogeneous part on the boundary into a lateral force within the governing function by the Dirac operator,which linearizes and homogenizes the original bound-ary,allowing one to employ the modal superposition method for obtaining solutions to reconstructive governing equations.Once projected into the modal space,the harmonic balance method(HBM)is utilized to solve coupled ordinary differential equations(ODEs)of truncated systems with nonlinearity.To validate the convergence and accuracy of the proposed Dirac method,the results of typical examples,involving nonlinearly restricted boundaries,moment excitation,and displacement excitation,are compared with those of the differential quadrature element method(DQEM).The results demonstrate that when dealing with nonlinear boundaries,the Dirac method exhibits more excellent accuracy and convergence compared with the DQEM.However,when facing displacement exci-tation,there exist some discrepancies between the proposed approach and simulations;nevertheless,the proposed method still accurately predicts resonant frequencies while being uniquely capable of handling nonuniform displacement excitations.Overall,this methodology offers a convenient way for addressing nonlinear and non-homogenous plate boundaries.
      原文链接:
    • 万方数据
    • 维普

    Effect of boundary conditions on shakedown analysis of heterogeneous materials

    Xiuchen GONGYinghao NIEGengdong CHENGKai LI...
    39-68页
    查看更多>>摘要：The determination of the ultimate load-bearing capacity of structures made of elastoplastic heterogeneous materials under varying loads is of great importance for engineering analysis and design.Therefore,it is necessary to accurately predict the shakedown domains of these materials.The static shakedown theorem,also known as Melan's theorem,is a fundamental method used to predict the shakedown domains of structures and materials.Within this method,a key aspect lies in the construction and application of an appropriate self-equilibrium stress field(SSF).In the structural shake-down analysis,the SSF is typically constructed by governing equations that satisfy no external force(NEF)boundary conditions.However,we discover that directly applying these governing equations is not suitable for the shakedown analysis of heterogeneous ma-terials.Researchers must consider the requirements imposed by the Hill-Mandel condition for boundary conditions and the physical significance of representative volume elements(RVEs).This paper addresses this issue and demonstrates that the sizes of SSFs vary under different boundary conditions,such as uniform displacement boundary conditions(DBCs),uniform traction boundary conditions(TBCs),and periodic boundary conditions(PBCs).As a result,significant discrepancies arise in the predicted shakedown domain sizes of heterogeneous materials.Built on the demonstrated relationship between SSFs under different boundary conditions,this study explores the conservative relationships among different shakedown domains,and provides proof of the relationship between the elastic limit(EL)factors and the shakedown loading factors under the loading domain of two load vertices.By utilizing numerical examples,we highlight the conservatism present in certain results reported in the existing literature.Among the investigated bound-ary conditions,the obtained shakedown domain is the most conservative under TBCs.Conversely,utilizing PBCs to construct an SSF for the shakedown analysis leads to less conservative lower bounds,indicating that PBCs should be employed as the preferred boundary conditions for the shakedown analysis of heterogeneous materials.
      原文链接:
    • 万方数据
    • 维普

    Effects of layer interactions on instantaneous stability of finite Stokes flows

    Chen ZHAOZhenli CHENC.T.MUTASADong LI...
    69-84页
    查看更多>>摘要：The stability analysis of a finite Stokes layer is of practical importance in flow control.In the present work,the instantaneous stability of a finite Stokes layer with layer interactions is studied via a linear stability analysis of the frozen phases of the base flow.The oscillations of two plates can have different velocity amplitudes,initial phases,and frequencies.The effects of the Stokes-layer interactions on the stability when two plates oscillate synchronously are analyzed.The growth rates of two most unsta-ble modes when δ＜0.12 are almost equal,and δ=δ*/h*,where δ*and h*are the Stokes-layer thickness and the half height of the channel,respectively.However,their vorticities are different.The vorticity of the most unstable mode is symmetric,while the other is asymmetric.The Stokes-layer interactions have a destabilizing effect on the most unstable mode when δ＜0.68,and have a stabilizing effect when δ＞0.68.However,the interactions always have a stabilizing effect on the other unstable mode.It is explained that one of the two unstable modes has much higher dissipation than the other one when the Stokes-layer interactions are strong.We also find that the stability of the Stokes layer is closely related to the inflectional points of the base-flow velocity profile.The effects of inconsistent velocity-amplitude,initial phase,and frequency of the oscillations on the stability are analyzed.The energy of the most unstable eigenvector is mainly distributed near the plate of higher velocity amplitude or higher oscillation frequency.The effects of the initial phase difference are complicated because the base-flow velocity is extremely sensitive to the initial phase.
      原文链接:
    • 万方数据
    • 维普

    Dynamic performance and parameter optimization of a half-vehicle system coupled with an inerter-based X-structure nonlinear energy sink

    Yong WANGPeili WANGHaodong MENGLiqun CHEN...
    85-110页
    查看更多>>摘要：Inspired by the demand of improving the riding comfort and meeting the lightweight design of the vehicle,an inerter-based X-structure nonlinear energy sink(Ⅸ-NES)is proposed and applied in the half-vehicle system to enhance the dynamic perfor-mance.The X-structure is used as a mechanism to realize the nonlinear stiffness charac-teristic of the NES,which can realize the flexibility,adjustability,high efficiency,and easy operation of nonlinear stiffness,and is convenient to apply in the vehicle suspension,and the inerter is applied to replacing the mass of the NES based on the mass amplification characteristic.The dynamic model of the half-vehicle system coupled with the Ⅸ-NES is established with the Lagrange theory,and the harmonic balance method(HBM)and the pseudo-arc-length method(PALM)are used to obtain the dynamic response under road harmonic excitation.The corresponding dynamic performance under road harmonic and random excitation is evaluated by six performance indices,and compared with that of the original half-vehicle system to show the benefits of the Ⅸ-NES.Furthermore,the structural parameters of the Ⅸ-NES are optimized with the genetic algorithm.The re-sults show that for road harmonic and random excitation,using the Ⅸ-NES can greatly reduce the resonance peaks and root mean square(RMS)values of the front and rear sus-pension deflections and the front and rear dynamic tire loads,while the resonance peaks and RMS values of the vehicle body vertical and pitching accelerations are slightly larger.When the structural parameters of the Ⅸ-NES are optimized,the vehicle body vertical and pitching accelerations of the half-vehicle system could reduce by 2.41％and 1.16％,respectively,and the other dynamic performance indices are within the reasonable ranges.Thus,the Ⅸ-NES combines the advantages of the inerter,X-structure,and NES,which improves the dynamic performance of the half-vehicle system and provides an effective option for vibration attenuation in the vehicle engineering.
      原文链接:
    • 万方数据
    • 维普

    Multi-blade rubbing characteristics of the shaft-disk-blade-casing system with large rotation

    Zhiyuan WULinchuan ZHAOHan YANGe YAN...
    111-136页
    查看更多>>摘要：Blade rubbing faults cause detrimental impact on the operation of aero-engines.Most of the existing studies on blade rubbing in the shaft-disk-blade-casing(SDBC)system have overlooked the elastic deformation of the blade,while some only consider the whirl of the rotor,neglecting its spin.To address these limitations,this paper proposes a dynamic model with large rotation for the SDBC system.The model incorporates the spin and whirl of the rotor,enabling the realistic reproduction of multi-blade rubbing faults.To verify the accuracy of the SDBC model with large rotation and demonstrate its capability to effectively consider the rotational effects such as the centrifugal stiffening and gyroscopic effects,the natural characteristics and dynamic re-sponses of the proposed model are compared with those obtained from reported research and experimental results.Furthermore,the effects of the rotating speed,contact stiffness,and blade number on the dynamic characteristics of the SDBC system with multi-blade rubbing are investigated.The results indicate that the phase angle between the rotor de-flection and the unbalance excitation force increases with the increasing rotating speed,which significantly influences the rubbing penetration of each blade.The natural fre-quency of the SDBC system with rubbing constrain can be observed in the acceleration response of the casing and the torsional response of the shaft,and the frequency is related to the contact stiffness.Moreover,the vibration amplitude increases significantly with the product of the blade number under rubbing,and the rotating frequency approaches the natural frequency of the SDBC system.The proposed model can provide valuable insight for the fault diagnosis of rubbing in bladed rotating machinery.
      原文链接:
    • 万方数据
    • 维普

    Galerkin-based quasi-smooth manifold element(QSME)method for anisotropic heat conduction problems in composites with complex geometry

    Pan WANGXiangcheng HANWeibin WENBaolin WANG...
    137-154页
    查看更多>>摘要：The accurate and efficient analysis of anisotropic heat conduction problems in complex composites is crucial for structural design and performance evaluation.Tradi-tional numerical methods,such as the finite element method(FEM),often face a trade-off between calculation accuracy and efficiency.In this paper,we propose a quasi-smooth manifold element(QSME)method to address this challenge,and provide the accurate and efficient analysis of two-dimensional(2D)anisotropic heat conduction problems in composites with complex geometry.The QSME approach achieves high calculation preci-sion by a high-order local approximation that ensures the first-order derivative continuity.The results demonstrate that the QSME method is robust and stable,offering both high accuracy and efficiency in the heat conduction analysis.With the same degrees of freedom(DOFs),the QSME method can achieve at least an order of magnitude higher calcula-tion accuracy than the traditional FEM.Additionally,under the same level of calculation error,the QSME method requires 10 times fewer DOFs than the traditional FEM.The versatility of the proposed QSME method extends beyond anisotropic heat conduction problems in complex composites.The proposed QSME method can also be applied to other problems,including fluid flows,mechanical analyses,and other multi-field coupled problems,providing accurate and efficient numerical simulations.
      原文链接:
    • 万方数据
    • 维普

    Dynamic and electrical responses of a curved sandwich beam with glass reinforced laminate layers and a pliable core in the presence of a piezoelectric layer under low-velocity impact

    N.SHAHVEISIS.FELI
    155-178页
    查看更多>>摘要：The dynamic responses and generated voltage in a curved sandwich beam with glass reinforced laminate(GRL)layers and a pliable core in the presence of a piezo-electric layer under low-velocity impact(LVI)are investigated.The current study aims to carry out a dynamic analysis on the sandwich beam when the impactor hits the top face sheet with an initial velocity.For the layer analysis,the high-order shear deformation theory(HSDT)and Frostig's second model for the displacement fields of the core layer are used.The classical non-adhesive elastic contact theory and Hunter's principle are used to calculate the dynamic responses in terms of time.In order to validate the analyt-ical method,the outcomes of the current investigation are compared with those gained by the experimental tests carried out by other researchers for a rectangular composite plate subject to the LVI.Finite element(FE)simulations are conducted by means of the ABAQUS software.The effects of the parameters such as foam modulus,layer material,fiber angle,impactor mass,and its velocity on the generated voltage are reviewed.
      原文链接:
    • 万方数据
    • 维普

    Frictional contact analysis of a rigid solid with periodic surface sliding on the thermoelectric material

    Yali ZHANGYueting ZHOUShenghu DING
    179-196页
    查看更多>>摘要：Understanding and characterizing rough contact and wavy surfaces are essential for developing effective strategies to mitigate wear,optimize lubrication,and enhance the overall performance and durability of mechanical systems.The sliding friction contact problem between a thermoelectric(TE)half-plane and a rigid solid with a periodic wavy surface is the focus of this investigation.To simplify the problem,we utilize mixed boundary conditions,leading to a set of singular integral equations(SIEs)with the Hilbert kernels.The analytical solutions for the energy flux and electric current density are obtained by the variable transform method in the context of the electric and temperature field.The contact problem for the elastic field is transformed into the second-kind SIE and solved by the Jacobi polynomials.Notably,the smoothness of the wavy contact surface ensures that there are no singularities in the surface contact stress,and ensures that it remains free at the contact edge.Based on the plane strain theory of elasticity,the analysis primarily examines the correlation between the applied load and the effective contact area.The distribution of the normal stress on the surface with or without TE loads is discussed in detail for various friction coefficients.Furthermore,the obtained results indicate that the in-plane stress decreases behind the trailing edge,while it increases ahead of the trailing edge when subjected to TE loads.
      原文链接:
    • 万方数据
    • 维普

    Semi-analytical investigation of heat transfer in a porous convective radiative moving longitudinal fin exposed to magnetic field in the presence of a shape-dependent trihybrid nanofluid

    C.G.PAVITHRAB.J.GIREESHAM.L.KEERTHI
    197-216页
    查看更多>>摘要：The thermal examination of a non-integer-ordered mobile fin with a mag-netism in the presence of a trihybrid nanofluid(Fe3O4-Au-Zn-blood)is carried out.Three types of nanoparticles,each having a different shape,are considered.These shapes include spherical(Fe3O4),cylindrical(Au),and platelet(Zn)configurations.The combination approach is utilized to evaluate the physical and thermal characteristics of the trihybrid and hybrid nanofluids,excluding the thermal conductivity and dynamic viscosity.These two properties are inferred by means of the interpolation method based on the volume fraction of nanoparticles.The governing equation is transformed into a dimensionless form,and the Adomian decomposition Suinudu transform method(ADSTM)is adopted to solve the conundrum of a moving fin immersed in a trihybrid nanofluid.The obtained results agree well with those numerical simulation results,indicating that this research is reliable.The influence of diverse factors on the thermal overview for varying noninte-ger values of γ is analyzed and presented in graphical representations.Furthermore,the fluctuations in the heat transfer concerning the pertinent parameters are studied.The results show that the heat flux in the presence of the combination of spherical,cylindri-cal,and platelet nanoparticles is higher than that in the presence of the combination of only spherical and cylindrical nanoparticles.The temperature at the fin tip increases by 0.705 759％when the value of the Peclet number increases by 400％,while decreases by 11.825 13％when the value of the Hartman number increases by 400％.
      原文链接:
    • 万方数据
    • 维普